Transmission network



Jan. 23, 1934. H: w BODE 1,944,209

TRANSMISSION NETWORK Filed July 6, 1932 INVENTOR H. W 8005 A T TORNE K Patented Jan. 23, 1934 Miran STATES.

TRANSMISSION NETWORK I Hendrik W. Bode, New York, N. Y., assignor to Bell Telephone Laboratories,

Incorporated,

New York, N. Y., a. corporation of New York Application July 6, 1932. Serial No. 621,008

6 Claims.

This invention relates to wave transmission networks and more particularly to reactance networks, such as wave filters, of the unbalanced type in which one side of the circuit may be grounded.

It is well known that the symmetrical lattice type of network in its generalized form can be so designed as to have the same wave transmission properties asany other symmetrical fourterminal network. While this type of network therefore has the greatest possible diversity of transmission characteristics it is limited in its usefulness by the fact that it can not be readily adapted to unbalanced circuits and because of the duplication of impedance elements it involves.

The present invention provides a reactancenetwork of the unbalanced type which has substantially the same degree of generality in respect to its transmission characteristics as a symmetrical lattice including only reactance elements.

The network of the invention consists of a bridged-T network in which the series branches of the T are two equal inductances of finite value coupled together with unity coupling, in combination with a pair of equal impedances connected in series external to. the bridged-T. The bridging arm and the shunt arm of the bridged-T are not restricted in character except to the extent that they should consist of reactance elements. The series impedances external to the bridged-T in general will consist only of simple capacitance elements but in certain cases may comprise simple combinations of inductance and capacitancein series.

The nature of the invention will be more fully understood by referring to the following detailed description and to the attached drawing, forming a part thereof, in which;

Figs. 1 and 5 show two general forms of the network of the invention;

Figs. 2, 3, 4, 6 and '7 are schematic diagrams to which reference is made in explaining the invention, and

Fig. 8 represents a specific embodiment of the invention in a wave filter.

The network of Fig. 1, which represents one general form of the invention, comprises a line impedance group made up of a generalized reactance 2X5. shunted by an inductance of value 2La and having two end impedances constituted by condensersof capacity Ca, and a shunt imped ance group consisting of a condenser of capacity 2Cb in series with a parallel combination of an inductance of, value and a second generalized reactance The shunt group is connected between the midpoint of the inductance ZLa'and the other side of the network, the arrangement constituting a bridged-T'system with external impedances added outside the bridge. The two halves of the coil 2L2, are coupled together with unity coupling, for example, by bifilar winding, so that the coil acts as a perfectly coupled transformer of finite inductance. I

The network is equivalent in its transmission properties to a symmetrical lattice of the general type shown in Fig. 2, the branch impedances Z1 and Z2 of which have the form and values shown in Figs. 3 and 4 respectively. In Fig. 4 the capacity Cb is'equal to the eifective capacity of Ca and Cb connected in series, or

The propagation constant P and the characteristic impedance K of the lattice of Fig. 2, and hence, by virtue of the equivalence, of the network of Fig. 1, are given by the formulae It is to be noticed that Equation (1) is not altered by the interchange of Z1 and Z2 except that a phase change of 1hr radians may occur. Physically this means that the impedances Z1 and Z2 may beinterchanged in the network of Fig. 2 without affecting the transmission properties otherwise than by introducing a phase reversal of the output currents.

By known theorems relating to reactances, for which reference is made to the Bell System Technical Journal, vol. III, No. 2, April, 1924, A Reactance Theorem, by R. M. Foster, it may be shown that any combination of diverse reactance elements may be transformed to an equivalent combination of the type shown in Figs. 3 and 4 provided the capacities Ca or Cb are permitted to assume any value finite or infinite. Thus, a simple series resonant combination may be obtained by making the reactance X8. in Fig. 3 infinite and a simple parallel resonant combination may be obtained by making Xa a simple capacity and Ca infinitely great.

The steps to be taken in converting any reactive impedance into the form shown by Figs. 3 and 4, in accordance with the method described by Foster in the above mentioned article, are as follows: In Equation (1) of his article Foster gives the general expression for the reactance S, using his notation,

(1 1 1 (Pa P (p2n-1 p) 3 S p(p2 p (pa-2 -p If, in accordance with his general method, the reactance is represented by a chain of anti-reso nant loops connected in series, then the network will include a series condenser C of value P2 P4 P2nz ,C HP12P32 Inn-1 (4) It will be noted that in the special case where 191:0, then C will be infinite, that is, absent from the chain.

. The reactance S of the network with C removed is given by the expression work of the type of Fig. 1, the line capacities Ca having any value finite or infinite. The procedure in the conversion is first of all to transform the impedances Z1 and Z2 to the form of Figs. 3 and 4, Usually it is simplest in the initial design to determine Z1 and Z2 as chains of antiresonant circuits or as parallel connected systems of series resonant circuits, in accordance with the rules given in the aforementioned article by Foster. The transformation may be carried out by analytical methods or by a step-by-step application of the elementary substitutions and transformation formula given in the Bell System Technical Journal, vol. II, No. 1, January, 1923, pages 45 and 46. Whatever the initial form of these impedances may be the determination of the capacities Ca and Cb is always simple, these being the total effective capacities of the impedances at zero frequency.

After converting the impedances to the desired form, the one having the larger series capacity is used as the basis of the design of the line impedance group of the network of Fig. l. The remainder of the conversion follows naturally from the impedance relationships indicated by the figures. The choice of either one or the other of the impedances for the line group of Fig. 1 does not affect the transmission properties of the resulting network otherwise than by introducing a phase reversal of the output currents, as already described.

In certain cases it will be found that one or possibly both of the impedances Z1 and Z2 have no series capacity, that is, the series capacities are infinite and have zero reactance. In such cases the resulting unbalanced network reduces to one of known type.

Another general form of the invention is shown The numerator of the expression on the right hand side of Equation (5 is a polygnomial in 10 whose roots can be obtained by standard mathematical processes. If the roots are designated ps ps then the numerator can be rewritten as where H is some new constant. The reactance S then becomes S 1Hp (1 2 1 (1 4 1 (pa-2 p (6) From the mode of derivation this is the reactance of a physical network, and it can be built by Fosters methods as a set of resonant branches connected in parallel, including a parallel inductance L given by pu pb p, L H P2 1 4 Pat-2 (7) The inductance L of Equation ('7) is the inductance La or Lb of Figs. 3 and 4, while the remainder of the parallel resonant branches are represented by the reactance Xa or Xb of those figures.

If, now, a reactance network is designed as a lattice to meet a given set of requirements, for example, in accordance with the principles set forth in my earlier Patent 1,828,454 issued 00- tober 20, 1931, it follows that such a lattice can always be transformed into an unbalanced netin Fig. 5, which diifers from the network of Fig. 1 in having a condenser of capacity added in shunt with the inductance 2La, an additional inductance Lc in series with each end impedance Ca, an inductance 1125 In this way the theoretical transmission properties of the equivalent lattice, given by Equations (1). and (2), may be realized very closely in the generalized bridged-T network. In order for the network to be physically realizable it is necessary 15,0

that the impedance Z1, used as the basis of the design of the line impedance group of the network of Fig. 5. shall have the larger series capacity Ca and the smaller series inductance Lo, as compared with the corresponding elements Cb and La of impedance Z2.

The transmission properties of the network of the invention depend, as stated above, upon the characteristics of the impedances Z1 and Z2. For example, if the reactance 2Xa of Fig. 5 consists of two series resonant branches connected in parallel and the reactance is a simple series resonant branch, then the network shown in Fig. 8 will result. In this figure the reactance 2Xa is constituted by the parallel connected resonant circuits ZLe,

and 2L1,

and the reactance by the single resonant circuit 20 The other parts of the network correspond to Fig. 5. The branches of the equivalent lattce structure are readily found as indicated above. To design the structure as a band-pass filter, the method described in my aforementioned Patent No. 1,828,454 may be followed for the determinaton of the values of the impedance elements of the equivalent lattice. Conversion to the bridged-T structure may then be accomplished as explained above.

What is claimed is:

1. A wave transmission network comprising a bridged-T network and a pair of equal reactances connected in series therewith, one on each side thereof, the series arms of said bridged-T being constituted by a pair of equal finite inductances inductively coupled, and the shunt arm and the bridging arm of said bridged-T being lumped impedances of different characteristics.

2. A wave transmission network comprising a bridged-T network and a pair of equal reactances connected in series therewith, one on each side thereof, the series arms of said bridged-T being constituted by a pair of equal finite inductances coupled series aiding with unity coupling factor, and the shunt arm and the bridging arm of said bridged-T comprising reactive impedances of different characteristics.

3. A wave filter comprising a bridged-T network and a pair of equal reactances connected in series therewith, one on each side thereof, the series arms of said bridged-T being constituted by a pair of equal finite inductances coupled series aiding with unity coupling factor, and the shunt arm and the bridging arm of said bridged-T comprising reactive impedances of different characteristics, said equal reactances being so proportioned with respect to said reactive impedances that said filter transmits with negligible attenuation currents of all frequencies lying between the upper limiting frequency and the lower limiting frequency of the range of frequencies to be transmitted, while approximately extinguishing currents of neighboring frequencies lying outside of said limiting frequencies.

4. A transmission network comprising a bridged-T network and two equal capacitances connected in series with said bridged-T, one on each side, the series arms of said bridged-T consisting of a pair of equal finite inductances coupled series aiding, and the shunt arm and the bridging arm of said bridged-T comprising reactive impedances of different characteristics.

5. A wave transmission network comprising a bridged-T network and a pair of equal reactances connected in series therewith, one on each side thereof, each of said reactances comprising a capacitance and an inductance connected in series relation, the series arms of said bridged-T being constituted by a pair of equal finite inductances coupled series aiding with substantially unity coupling factor, and the shunt arm and the bridging arm of said bridged-T comprising reactive impedances of different characteristics.

6. A wave transmission network comprising a bridged-T network and a pair of equal reactances connected in series therewith, one on each side thereof, each of said reactances comprising a capacitance and an inductance connected in series relation, the series arms of said bridged-T consisting of a pair of finite inductances inductively coupled, the bridging arm of said bridged-T comprising a reactive impedance in parallel with a capacitance, the value of said last-mentioned capacitance being adjusted to compensate for the interwinding capacitance of said pair of coupled inductances.

HENDRIK W. BODE. 

